Two-dimensional Fracture Networks Research Articles

Volcanic weathered crust reservoir analog: Insights from fault-controlled fracture permeability in the trachytic rocks of the Pernambuco Basin, NE Brazil

Naturally fractured volcanic rocks represent a globally significant potential hydrocarbon reservoirs and can also be used for CO2 storage; however, the study of volcanic reservoirs in Brazil is limited. Although numerous volcanic reservoir types have been classified, relatively few studies are dedicated to the weathering of crust-like reservoirs, i.e., volcanic rocks undergoing subaerially alteration by weathering prior to deep burial. This study aims to characterize a volcanic weathered crust reservoir analog located in the coastal zone of the Pernambuco Basin, NE Brazil. We applied a multiscale approach motivated by the expressive potential of volcanic rocks as reservoirs in this marginal basin and considered their implications for CO2 geological storage projects. The deformational aspects observed in this analog have also been observed in other volcanic rocks that crop out in the coastal zone, thus, the data provided here can guide future characterization of both onshore and offshore reservoirs. We focused on an 80 m wide outcrop and employed geometric and topological analysis of two-dimensional fracture networks to investigate the influence of regional fault zone control on the fracture permeability tensors. The parameters of fracture systems were studied using terrestrial gravimetric data, orthophoto mosaic obtained by an unmanned aerial vehicle (UAV), petrography, and outcrop-based structural data. The investigated outcrop includes porphyritic trachytes with euhedral sanidine crystals and minor quartz phenocrysts, sourced from the Ipojuca Magmatic Suite. The residual Bouguer map indicates the influence of at least two regional rift fault zones, i.e., NW-SE (strike-slip) and NE-SW (normal) trending systems, in the studied rocks. These trachytic rocks exhibited a marked dissolution of sanidine phenocrysts and matrix, columnar disjunctions, and natural fractures, causing the porosity and permeability of the reservoir analog to increase. Geometric and topological analyses showed that the south-central sector of the outcrop exhibits heightened connectivity within the fracture network. Furthermore, the principal fracture permeability is controlled by the primary families of the fracture network and regional fault zones. Our results demonstrate that the fracture network observed in the volcanic reservoir analog was influenced by the post-rift tectonic reactivation of Cretaceous structures within the Pernambuco Basin. The secondary porosity resulting from weathering and subsequent dissolution of the primary constituents and fractures of the rocks studied demonstrates the potential for the exploration of these reservoirs as models for known occurrences of volcanic rocks in the onshore and offshore domains of the Pernambuco Basin.

Data-driven hydraulic property analysis and prediction of two-dimensional random fracture networks

The large parameter space and uncertainty of the discrete fracture networks (DFNs) make the hydraulic characteristics have multiple possibilities. Statistical analysis of hydraulic characteristics based on a large amount of data is a standard practice and central to DFN methodology. The present study developed a two-dimensional (2D) DFN numerical seepage model based on Matlab and Comsol from modeling and parameter calculation to simulation to investigate the influence of parameters involved fracture network on seepage characteristics of DFNs. In total, 1728 2D DFN models were generated with increasing fracture density, fracture length, power-law exponent, fracture orientations, and fracture included angles, and 1728 × 3 = 5184 numerical simulations of fluid flow along the x-axis, y-axis, and center through the DFN models are conducted using a self-developed numerical code. The influence of fracture geometric features on connectivity and permeability are estimated, respectively. And to realize the prediction of permeability tensor by known geological data, a theoretical model based on the Snow model and a data mining model based on the back-propagation model are discussed. The analysis helps researchers and engineers can make informed decisions and develop effective strategies for addressing the challenges posed by uncertainty hydraulic property of the fractured rock masses.

A Two-Dimensional Planar Fracture Network Model for Broken Rock Mass Based on Packer Test and Fractal Dimension

Broken rock masses with the complexity and concealment widely exist in nature such as underground mine, collapse column, and zone. It is extremely difficult to model fracture networks and to simulate water diffusion for broken rock masses. To explore a reasonable fracture network model for broken rock masses, a new method for modeling a two-dimensional planar fracture network model is proposed in this paper. It includes packer test, empirical relationship, fractal width description, and symmetric expansion modeling. Then, the fluid-solid coupling is used to simulate the diffusion properties of water in the two-dimensional planar fracture network model. It is found that the diffusion velocities vmax and vmin do not appear in the fracture widths λmax and λmin. It indicates that the fracture widths λmax and λmin in the fracture network model for broken rock mass have little impact on the diffusion velocity. Furthermore, the fracture distribution pattern in the fracture network model is an important factor affecting the diffusion velocities vmax and vmin. The simulation results of water diffusion in the currently proposed model are almost consistent with the actual process of the packer test. Also, the validity of the two-dimensional planar fracture network model is verified by comparing the simulation results with the existing research.

XFVM modelling of fracture aperture induced by shear and tensile opening.

In reservoir simulation, it is important to understand the mechanical behaviour of fractured rocks and the effect of shear and tensile displacements of fractures on their aperture. Tensile opening directly enhances the fracture aperture, whereas shear of a preexisting rough-walled fracture creates aperture changes dependent on the local stress state. Since fracture dilatation increases reservoir permeability, both processes must be included in a realistic and consistent manner into the mechanical reservoir simulation model. Here, we use the extended finite volume method (XFVM) to conduct flow and geomechanics simulations. In XFVM, fractures are embedded in a poroelastic matrix and are modelled with discontinuous basis functions. On each fracture segment the tractions and compressive forces are calculated, and one extra degree of freedom is added for both the shear and tensile displacement. In this particular XFVM implementation we assume that linear elasticity and steady state fluid pressure adequately constrain the effective stress. In this paper, shear dilation is not calculated a posteriori, but it enters the equations such that aperture changes directly affect the stress state. This is accomplished by adding shear dilation to the displacement gradients and therefore ascertains a consistent representation in the stress-strain relations and force balances. We illustrate and discuss the influence of this extra term in two simple test cases and in a realistic layer-restricted two-dimensional fracture network subjected to plausible in situ stress and pore pressure conditions.

Propagation and sealing efficiency of chemical grouting in a two-dimensional fracture network with flowing water

In this study, an orthogonal array experiment is conducted by using a transparent fracture network replica. Image processing and theoretical analysis are performed to investigate the model sealing efficiency (SE), factors influencing SE, and the effect of flowing water on propagation. The results show that grout propagation can be classified into three patterns in the fracture network: sealing off, partial sealing, and major erosion. The factors controlling the SE in a descending order of the amount of influence are the initial water flow speed, fracture aperture, grout take, and gel time. An optimal value for the combination of the gel time and grout take (artificial factors) can result in a good SE. The grouting and seepage pressures are measured, and the results reveal that their variations can indicate the SE to some extent. The SE is good when the seepage pressure at each point increases overall; the frequent fluctuations in the seepage pressure indicate a moderately poor SE, and an overall decline in the seepage pressure indicates a major erosion type. The deflection effect of grouting shows an approximately elliptical propagation with the long axis expanding along the wider fracture opening, demonstrating further application in grouting design.

Evolving geometries, topologies, and apertures in fracture networks: Quantitative insights from lattice modeling

Fracture networks are crucial in controlling rock mass permeability. Some of the important features of the fracture networks like the density, interconnectivity, spatial distribution, and fracture apertures determine the success of the subsurface operations. Fracture networks can be studied with analogue studies, physical experiments, and numerical modeling. In this study, we analyse the evolution of a two-dimensional fracture network under gravitational and shear loads using the lattice modeling capabilities of the microstructural modeling environment “Elle”. The simulation cases include varying gravitational loads and Young’s moduli of the formations. The topological progression of the modeled fracture network from isolated to interconnected nodes depicts a realistic network evolution process. The study shows that the rock stiffness exhibits a direct correlation with the number of fractures influencing the average aperture size of the network. A higher gravity load resulted in the development of a sparse fracture network. Stiffer rock models also showed an early onset of fracturing.

Impacts of T-type intersections on the connectivity and flow in Complex two-dimensional fracture networks

Natural fractures usually form T-type intersections, but the impacts of T-type intersections on the connectivity and flow results (such as permeability and fluid production) in complex fracture networks are rarely investigated. Here, a stochastic discrete fracture network method is implemented to construct complex two-dimensional fracture networks, denoted as original fracture networks. By implementing the rule-based fracture growth algorithm, the corresponding kinematic fracture networks are generated with a substantial proportion of T-type intersections. The connectivity and flow results of both the single-phase and two-phase flow simulations in these two types of fracture networks are systematically investigated. The results show that kinematic fracture networks tend to connect more fractures with fewer intersections and yield better connectivity than the original ones. Most kinematic fracture networks have larger permeability in the single-phase flow simulation and higher cumulative gas production in the two-phase flow simulation than original fracture networks under the same boundary conditions. The proportions of permeability and production enhancement are 68% and 77%, respectively. Flow results have strong positive correlations with the connectivity of fracture networks, but they are nonequivalent and strongly impacted by the number of inlets and outlets.

Deterioration laws of Hoek-Brown parameters in freeze–thaw multi-fractured rock mass

The Hoek-Brown criterion can better depict the nonlinear failure characteristics of rock mass, which has been widely used in the fields of large-scaled slopes, deep-buried tunnels, foundations in complex geological conditions, hydropower dams, and energy mining. In view of the previous studies mostly focused on the property reduction of freeze–thaw rock, the deterioration study of Hoek-Brown parameters for freeze–thaw multi-fractured rock mass was investigated in this study. Firstly, Monte-Carlo method was used to generate two-dimensional discrete fracture network, according to which the multi-fractured rock-like samples were prepared. Freeze-thaw cycle experiments were subsequently designed and executed to observe the apparent damage of freeze–thaw effect on the samples. Then, laboratory direct shear tests on freeze–thaw samples under multistage normal loading were carried out. The shear performances of freeze–thaw rock mass were analyzed based on the shear stress-shear displacement curves of samples with different freeze-thawed cycles. Besides, considering the deficiencies of the existing Hoek-Brown parameter estimation methods such as complicated sample preparation and strong subjectivity, a new estimation method based on shear test was proposed by deducing the shear expression of Hoek-Brown criterion, which was programmed in MATLAB and verified by direct shear test results. On this basis, the values of Hoek-Brown parameter of those samples under different freeze–thaw cycles were determined, and the variation law with freeze–thaw cycles was summarized. It turned out that the values of GSI and mi both decrease with the increase of freeze–thaw cycles, and the decreasing rate is also lowering, according with the negative exponential function model.

Laminar and turbulent groundwater flows in confined two- and three-dimensional discrete fracture networks

Using laminar or turbulent flow equations indiscriminately to describe groundwater flows in fracture networks may result in large errors. We propose a new method for simulating steady-state groundwater flows in two- and three-dimensional fracture networks by separating laminar flows and turbulent flows in individual fractures. Poiseuille's law is employed when the flow is laminar, while Swamee and Jain formula is utilized when the flow is turbulent. The model results are first compared to recently measured field groundwater flow data in a mining tunnel network. The effect of hydraulic gradient, aperture, fracture width in the third dimension, and fracture density is then examined. Using the laminar flow equation indiscriminately in all fractures overestimates groundwater flowrates, whereas using the turbulent flow equation underestimates them. The aperture contrast of large and small fractures has a significant impact on the potential errors of indiscriminately applying the laminar or turbulent flow equation and the flowrate difference between the three-dimensional and two-dimensional fracture networks. Total groundwater flowrates increase with fracture density in both three-dimensional and two-dimensional fracture networks, with the largest increase occurring when additional fractures are introduced parallel to the hydraulic gradient. The new approach may be utilized to estimate hydraulic head distribution and groundwater flowrate according to the crack patterns and geometric properties of the fractured rock.

Comparative study on interconnectivity between three-dimensional and two-dimensional discrete fracture networks: A perspective based on percolation theory

Two-dimensional (2-D) discrete fracture networks (DFNs) are widely used to study the hydraulic properties of fractured rock masses. There are few studies on the reliability of 2-D DFNs reflecting the hydraulic properties of three-dimensional (3-D) rock masses. This study provides a new perspective based on percolation theory to study the interconnectivity between 3-D and 2-D DFNs quantitatively. For isotropic fractured rock masses, the corresponding value of the number of fractures in per sampled volume (P30) when 3-D DFNs achieve the percolation threshold is theoretically derived. Additionally, the corresponding value of P30 of the original 3-D model when its 2-D DFNs on cutting planes achieve the percolation threshold is also derived for comparison. These theoretical formulas show that: (a) The corresponding values of P30 at percolation threshold for both 3-D and 2-D DFNs are only related to the fracture diameter and inversely proportional to its third power; and (b) The corresponding value of P30 when 2-D DFNs achieve the percolation threshold is 6.5 times of the corresponding value of P30 when its original 3-D DFNs achieve the percolation threshold. Numerical codes and experiments based on Particle Flow Code and Matlab are developed to verify the derived theoretical equations, and the results show that the theoretical equations are validated.

Thermo-Hydro-Mechanical Coupling Processes in Carbonate Geothermal Reservoirs and Their Numerical Simulation

Abstract Reinjecting low-temperature tailwater into geothermal reservoirs leads to complex thermo-hydro-mechanical coupling processes, making it more difficult to predict the thermal breakthrough of the reservoirs. By taking the example of the deep carbonate geothermal reservoirs of karst fissure type in the Xianxian geothermal field in China, this paper studied the thermo-hydro-mechanical coupling processes in the case of reinjection based on previous tracer tests. It established a thermo-hydro-mechanical three-field coupling model based on a two-dimensional discrete fracture network and further verified its suitability through inversion analyses. Moreover, this paper discovered the regularity of the effects of temperature and pressure changes on the deformation of the rock masses in geothermal reservoirs and clarified the mechanisms of the seepage and heat transfer in thermo-hydro-mechanical coupling processes. Meanwhile, it presented the effects of the pressure and temperature on the heat extraction efficiency and production well temperature of the geothermal production-reinjection system in the Xianxian geothermal field. As indicated by the results, the pressure and temperature of geothermal reservoirs increased and decreased, respectively, in the initial phase of the reinjection, leading to an increase in fracture aperture and reservoir permeability. Then, they tended to gradually stabilize, and the amplitude change of the reservoir permeability decreased as the reinjection proceeded. Finally, this paper proposed an optimized reinjection scheme of the study area, aiming to provide scientific support for geothermal reinjection.

A new subsampling methodology to optimize the characterization of two-dimensional bedrock fracture networks

This paper introduces a new subsampling method to determine the empirical relationships between the areal sampling coverage and the topological-geometric parameters resulting from characterization of two-dimensional outcrop fracture networks. We further developed these relationships into correlations between the total sampling coverage and variance of the characterization result, hence providing insight to the objective uncertainties related to fracture network characterization. The analyses were conducted using two new open-source Python packages: fractopo and fractopo-subsampling, designed for fracture network analysis and subsampling, respectively. We conducted the study on the well-exposed crystalline outcrops of Getaberget, Åland Islands, Finland, where a total of 42499 fracture traces were manually digitized from 13 circular target areas. For the purposes of subsampling, we conducted fracture network characterization for randomly located and sized subsample areas, which locate within the larger target areas.Based on our subsampling results we provide recommendations for the preliminary optimization of areal coverage used in outcrop fracture sampling and the use of our subsampling method for assessing the precision related to the areal fracture network characterization in other previously uncharacterized areas. As an example, we recommend using a total sampling area of 8000 m2 with 8 circular sampling areas to define the power-law exponents of fracture traces when conducting outcrop fracture network characterization with drone-based methodology done with similar initial sampling setup in comparable geological environments, as this coverage has shown an acceptable level of precision.

Progressive damage and fracture of biaxially-confined anisotropic coal under repeated impact loads

Coal masses in underground mines are in multiaxial stress states after excavation, and they are frequently subjected to dynamic loads particularly from continuous mining-induced seismic events. The changes of in-situ stress conditions and external dynamic loads may induce coal bursts, which involves the violent breaking of coal masses. Meanwhile, the coal bursting process may be influenced by bedding planes that are considered as unique structures in coal masses, which raises uncertainties of coal bursting mechanisms. This paper aims to reveal the progressive damage and burst proneness of anisotropic coal under coupled static stress and repeated dynamic loads. The tested coal specimens have five bedding plane orientations (β = 0°, 30°, 45°, 60°, and 90°), where β is the angle between the bedding plane and dynamic loading direction. A triaxial Hopkinson bar (Tri-HB) system is utilised to apply the biaxial static stress on the specimen and then followed by dynamic loading, and the stress and strain can be recorded by the system accordingly. After the loading test, ultrasonic wave velocity is measured to examine the degree of attenuation, and the quantification of microcrack characteristics is conducted by using the synchrotron-based X-ray computed tomography (CT). Then, the specimen is loaded again under the same biaxial static stress and dynamic load, and measured by ultrasonic sensors and X-ray CT. This process will be repeated until the final failure of the specimen. We found that both dynamic peak stress and P-wave velocity show a decreasing trend due to damage accumulation with increasing number of dynamic tests. The bearing capacities of anisotropic coal are mainly governed by bedding angles, for example, the specimen with β = 30° undergoes the lowest impact numbers, but the one with β = 90° can undergo the highest numbers. The crack initiation and propagation are progressively revealed by two-dimensional (2D) X-ray slices and 3D fracture network reconstructions. As impact number increases, both 2D and 3D fractal dimensions of cracks increase exponentially, whereas dynamic peak stress and P-wave velocity are negatively correlated with them.

Impact of horizontal spatial clustering in two-dimensional fracture networks on solute transport

This study explores the prevalence of fracture clustering in natural networks and its influence on fluid flow and advective transport. Fracture networks from a compilation of previously published maps that encompass igneous, metamorphic and sedimentary rock types, various geological and tectonic settings, and a broad distribution of length scales are analyzed using a two-point correlation technique to characterize the spatial scaling between fracture barycenters. The correlation dimension (Dc) ranges from 1.47 to 1.89 with a median of 1.8. These results suggest that fracture networks often exhibit spatial clustering and are rarely Poissonian as commonly assumed. Synthetic Discrete Fracture Networks (DFNs) with constant and variable transmissivity applied to all fractures are generated for three clustering (Dc = 1.6, Dc = 1.8, and Poissonian) and power law length exponent (α = 1.4, α = 1.8, and α = 2.2) scenarios. Median particle breakthrough times are shown to increase by 10–70% as spatial clustering transitions from Poissonian to highly clustered (Dc = 1.6). Median particle breakthrough times also increase, by a factor of 1.2–3.4 (20–240%), when the power law length exponent increases from α = 1.4 to α = 2.2. As clustering increases (i.e., Dc reduces), breakthrough curves become highly variable and exhibit features indicative of enhanced solute retention. The increase in median breakthrough times with clustering persists with different network size and transmissivity distribution. These results indicate that spatial clustering and length exponent both significantly influence transport. The use of power-law length distributions in generating fracture networks is relatively common, whereas the spatial organization of fractures is rarely included in transport studies of fractured rock. Structural heterogeneity introduced by spatially clustered organization of fractures leads to substantial complexity in flow paths which is not captured by Poissonian DFNs.

The relationships between permeability and geological entropy of fracture networks

A systematic approach has been proposed to estimate the relationship between the permeability and geological entropy of two-dimensional fracture networks. The relative entropy index is developed as a measure of multiple properties of two-dimensional fracture networks, including fracture density, length, orientation and spatial distribution. In order to understand geological entropy dependence of the permeability, a computational method combining fracture network generation and steady-state flow simulation is employed. Based on the results of detailed numerical simulations, the relative entropy index and permeability increase simultaneously as the fracture density and length are independently increased. A simple closed-form empirical expression of the logarithmic dependence of the normalized permeability on the relative entropy index is proposed.

Stress-Dependent Deformation and Permeability of a Fractured Coal Subject to Excavation-Related Loading Paths

The deformation and permeability of coal are largely affected by the presence and distribution of natural fractures such as cleats and bedding planes with orthogonal and abutting characteristics, resulting in distinct hydromechanical responses to stress loading during coal mining processes. In this research, a two-dimensional (2D) fracture network is constructed based on a real coal cleat trace data collected from the Fukang mine area, China. Realistic multi-stage stress loading is designed to sequentially mimic an initial equilibrium phase and a mining-induced perturbation phase involving an increase of axial stress and a decrease of confining stress. The geomechanical and hydrological behaviour of the fractured coal under various stress loading conditions is modelled using a finite element model, which can simulate the deformation of coal matrix, the shearing and dilatancy of coal cleats, the variation of cleat aperture induced by combined effects of closure/opening, and shear and tensile-induced damage. The influence of different excavation stress paths and directions of mining is further investigated. The simulation results illustrate correlated variations among the shear-induced cleat dilation, damage in coal matrix, and equivalent permeability of the fractured coal. Model results are compared with results of previous work based on conventional approaches in which natural fracture networks are not explicitly represented. In particular, the numerical model reproduces the evolution of equivalent permeability under the competing influence of the effective stress perpendicular to cleats and shear-induced cleat dilation and associated damage. Model results also indicate that coal mining at low stress rates is conducive to the stability of surrounding coal seams, and that coal mining in parallel to cleat directions is desirable. The research findings of this paper have important implications for efficient and safe exploitation of coal and coalbed methane resources.

Visualization of CO2 foam generation, propagation and sweep in a complex 2D heterogeneous fracture network

In this work, a visual two-dimensional (2D) heterogeneous fracture network model was designed to investigate CO2 foam generation, propagation and sweep with two different injection strategies (co-injection, COI; and surfactant solution alternating gas, SAG). In addition, gravitational effect was explored by this fracture model. In the case of the optimum foam quality (fg = 0.67), the results indicated the COI could form stable foam morphologies and differential pressures (ΔP), while the foam morphologies and ΔP showed a dynamic trend during each cycle of SAG. The ΔP of larger slug injection can establish 6–12 times than smaller slug injection in the fractured system. Because of CO2 breakthrough, the total sweep efficiency of continuous gas injection (CGI, 42%) and SAG (66%) were lower than COI (81%). Gravitational effect is insignificant during COI, whereas gravity has a considerable effect on SAG in terms of ΔP and sweep efficiency. As a result of gravitational effect, the entire ΔP curve decreased and required more fracture volume (FV) injected to achieve the final sweep efficiency during SAG. The results of this study provide preliminary observations that can provide new insights into mobility control by using CO2 foam in fractured tight reservoirs.

Topological analysis of fracture networks integrated with flow simulation models for equivalent fracture permeability estimation

Models that predict permeability by considering analogues of fractured media have been used to enhance the understanding of the relative contribution of fracture networks to reservoir quality. The analogue data can overcome scale limitations (sub-seismic to mm) and/or lack of consistency in subsurface datasets (e.g., seismic data, well logs, and cores). This paper presents a numerical tool (TopoScan), designed to process images of fractured systems based on topological methods to determine fracture attributes and automatically make these available for fracture modeling and numerical simulations. We use this program to carry out fracture modeling considering different topological patterns of two-dimensional synthetic fracture networks, with variable patterns of interconnection, aperture, and spatial organization. We used the finite element method for modeling the fracture system, with the incorporation of discontinuities for the representation of fractures in the medium. The models were used for numerical simulations of fluid flow (flow-based upscaling), and the results demonstrated that the influence of fractures interconnection degree (topological patterns) on the equivalent permeability of the fractured medium.

Anisotropic Propagation of Chemical Grouting in Fracture Network with Flowing Water.

This paper presents an experimental investigation on the propagation of chemical grouting in a two-dimensional permeated fracture network with various aperture widths. As grouting engineering is often concealed in most experiments, the propagation of grout in fractures is not fully understood. The anisotropic permeability of geological masses with different aperture widths was found and has been investigated since 1960. The deflection flow effect was first found by Tian for groundwater flow in two groups of fractures with different aperture widths. Field grouting indicated that the grout propagates along a group of fractures with larger apertures that are longer while propagating a shorter distance along fractures with small apertures. This phenomenon implies a deflection for grout propagation in fractures with different aperture widths. The results of our study confirm this and indicate that there would be an anisotropy of grout propagation when the two groups of aperture widths are different. The water flow conditions also cause the difference in grout propagation length. When the aperture widths of the two groups of fractures are the same, the propagation shows symmetrical ellipse propagation. The results show the anisotropy of the grout increases as the aperture width ratio increases. This study helps in understanding the mechanism of chemical grouting in fractures with different apertures and flowing water and outlines some implications for grouting design in a fractured rock mass.

Permeability Evolution of Two-Dimensional Fracture Networks During Shear Under Constant Normal Stiffness Boundary Conditions

The permeability evolution of fractal-based two-dimensional discrete fracture networks (DFNs) during shearing under constant normal stiffness (CNS) boundary conditions is numerically modeled and analyzed based on a fully coupled hydromechanical (HM) model. The effects of fractal dimension, boundary normal stiffness and hydraulic pressure on the evolutions of mechanical behaviors, aperture distributions and permeability are quantitatively investigated. The results show that with increasing confining pressure from 0 to 30 MPa, the permeability decreases from the magnitude of 10−13 m2 to 10−16 m2, which is generally consistent with previous models reported in the literature. With the increment of shear displacement from 0 to 500 mm, the variations in shear stress, normal stress and normal displacement exhibit the same patterns with the conceptual model. As shear advances, the permeability evolution exhibits a three-stage behavior. In the first stage, the permeability decreases due to the compaction of fractures induced by the increasing shear stress from 0 to the peak value. In the second stage, the permeability holds almost constant values under constant normal load (CNL) boundary conditions, whereas that under CNS boundary conditions decreases by approximately one order of magnitude. Under CNS boundary conditions, although the aperture of shearing fracture increases enhancing its own permeability, the apertures of surrounding fractures are compacted due to the simultaneous increases in the normal and shear stresses, which result in the decrease in the total permeability of DFNs. When the fractal dimension increases from 1.4 to 1.5, the permeability increases following exponential functions in the early stage of shear, which fail to characterize the permeability in the residual stage due to the complex flow path distributions. At the start of shear, the ratio of permeability perpendicular to the shear direction to that parallel to shear decreases approximately from 1.0 to 0.5 and then gradually decreases from 0.5 to 0.3 in the residual stage. The hydraulic pressure tends to open up the fractures and enhances the permeability. The magnitude in permeability enhancement is of approximately the same order with the increase in the hydraulic pressure.